School of Electrical and Computer Engineering

A Mathematical Theoryof Automatic Target

Recognition

Aaron D. Lanterman

(lanterma@ece.gatech.edu)

What Makes ATR “Harder” than Factoring Large Numbers?

• Factoring large numbers may be NP-hard, but...

• At least it’s easy to precisely specify what the problem is!

• Not so easy in ATR– Subject to controversy

Can You Build an Airplane Without a Theory of Aerodynamics?

• Sure! Without aerodynamic theory, you can do this...

• …but with a theory, you can do this!

Can You Build an Communication Systems w/out Information Theory?• Sure! Without Information Theory,

you can do this…

• …but with Information Theory, you can do this!

• Dick Blahut likens the situation to steam engines coming before the science of thermodynamics

• First steam engines build by entrepreneurs and “inventors”– Thomas Savery: 17th and 18th centuries– Necessity the mother of invention!

• Thermodynamics didn’t begin to crystallize until mid 19th century… but with it, you eventually get

Steam Engines and Thermodynamics

• Before Shannon, your boss might ask you to do the impossible, and fire you if you failed to do it!

• Your boss cannot fire your for failing to exceed channel capacity!

• You can tell your boss you need a better channel

• 1948: Claude Shannon’s “A Mathematical Theory of Communication” (1948) – Later renamed “The Mathematical Theory of

Communication”

• Found fundamental limits on what is possible, i.e. channel capacity

Shannon’s Lightning Bolt

shouldn’t

Theory and Technology• Advances in theory are not enough;

also need the technology

– Aerodynamic theory alone won’t get you a B-2;

need advances in materials, manufacturing

– Information theory along won’t get you cell phones;

need fast DSP chips, good batteries, even more theory (i.e. coding theory)

• Theory tells you what’s possible, but sometimes only hints at how to get there

– Quantum computing folks: does this sound familiar?

Info-Theoretic View of ATR

)(

)()|()|(

ˆ

yp

xpxypyxp

X

Source Channel Decoder

Hypothesis testing (LRT, GLRT) ML, Bayes, Neyman PearsonEstimation ML, MAP, M.M.S.E., Bayes

Miss, false alarm rate Confusion matrices Bias, Variance, M.S.E.

Optimality Criteria Performance Bounds

ChernoffStein’s Lemma

Cramer-Rao

Z

e )(

)(xE

xp

X

)|(

)|()|(

xyxyp

xyE

Z

e

Y ... ,Y ,Y = Y m21

Target Recognizer SceneUnderstanding

Multiple Sensors

Scene Synthesizer

Database

(Statistical Estimation-Theoretic)

CIS/MIM

What Makes ATR “Harder” than Designing a Cell Phone?

• The space of X for real-world scenes is extremely complicated

• You don’t get to pick p(x)

• Likelihood p(y|x) is difficult to formulate– The “channel” is often deliberately hostile

• Targets hiding in clutter• Using decoys and camouflage• Radars can be subject to jamming

• Geometric variability– Position– Orientation– Articulation– “Fingerprint”

• Environmental variability– Thermal variability in infrared– Illumination variability in visual

• Complexity variability– Number of objects not known

Variability in Complex Scenes

Ulf Grenander

• Student of Cramér (yes, that Cramér)

• PhD on statistical inference in function spaces (1950)

• “Toeplitz Forms and their Applications” (with Szegö)– Fundamental work on spectral estimation (1958)

• “Probabilities on Algebraic Structures” (1968)

• “Tutorial on Pattern Theory” - unpublished manuscript– Inspired classic paper by Geman & Geman (1983)

General Pattern Theory• Generalize standard probability,

statistics, and shape theory

• Put probability measures on complex structures– Biological structures

• Mitochondria• Amoebas• Brains• Hippocampus

– Natural language– Real-world scenes of interest in ATR

The 90’s GPT Renaissance

• Made possible by increases in computer power

• Michael Miller (Washington Univ., now at JHU) did a sabbatical with Grenander

• Fields Medalist David Mumford moves from Harvard to Brown; shifts from algebraic geometry to pattern theory

Composite Parameter Spaces

0

3 )3(k

kTypesSOx X

• Move away from thinking of detection, location, recognition, etc. as separate problems

kk TypesSO )3(3X

• Naturally handles obscuration• Don’t know how many targets are in the scene in advance

Applying the Grenander Program (1)

• Take a Bayesian approach

• Many ATR algorithms seek features that are invariant to pose (position and orientation)

• Grenander’s Pattern Theory treats pose as nuisance variable in the ATR problem, and deals with it head on– Co-estimate pose, or integrate it out

– At a given viewing angle, Target A at one orientation may look much like Target B at a different orientation

– “…the nuisance parameter of orientation estimation plays a fundamental role in determining the bound on recognition” - Grenander, Miller, & Srivastava

U. Grenander, M.I. Miller, and A. Srivastava, “Hilbert-Schmidt Lower Bounds for Estimators on Matrix Lie Groups for ATR,” IEEE Trans. PAMI, Vol. 20, No. 2, Aug. 1998, pp. 790-802.

Applying the Grenander Program (2)

• Develop statistical likelihood• Data fusion is natural

• At first, use as much of the data as possible– Be wary of preprocessing: edge extraction, segmentation etc.– Processing can never add information

• Data processing inequality from information theory

));(();( parametersdatafIparametersdataI

• If you need to extract features, i.e. for real-time computational tractability, try to avoid as much loss of information as possible

OCULARSGUYWITHBINMWIRLADAR LLLLL

Analytic Performance Bounds

• Estimation bounds on continuous parameters– Cramér-Rao bounds for continuous pose parameters– Hilbert-Schmidt metrics for orientation parameters

• Bounds on detection/recognition probabilities– Stein’s Lemma, Chernoff bounds– Asymptotic analysis to approximate probabilities of error– Performance in a binary test is dominated by a term exponential in a distance

measure between a “true” and an “alternate” target• Adjust pose of “alternate” target to get closest match to “true” target as seen by the

sensor system

– Secondary term involving CRB on nuisance parameters• Links pose estimation and recognition performance

U. Grenander, A. Srivastava, and M.I. Miller, “Asymptotic Performance Analysis of Bayesian Target Recognition,” IEEE Trans. Info. Theory, Vol. 46, No. 4, July 2000, pp. 1658-1665.

AnujSrivastava

Reading One of DARPA’s BAAs…

• DARPA’s E3D program seeks:

– “efficient techniques for rapidly exploiting 3-D sensor data to precisely locate and recognize targets.”

• BAA full of demands (hopes?) for different stages of the program, such as:

– “The Target Acquisition and Recognition technology areas will develop techniques to locate and recognize articulating, reconfigurable targets under partial obscuration conditions, with an identification probability of 0.85%, a target rejection rate less than 5%, and a processing time of 3 minutes per target or less”

…Leads Us to Wondering• If such a milestone is not reached, is that the fault of the algorithm or the sensor?

– How does the DARPA Program Manager know who to fire?– Without a theory, the DARPA PM may fire someone who was asked to

“exceed channel capacity,” i.e. given an impossible task

• What performance from a particular sensor is necessary to achieve a certain level of ATR performance,

independent of the question of what algorithm is used?

Perspective Projection

kk TypesSO )2(2X

Optical PSF

Poisson Photocounting Noise

Dead andSaturated Pixels

Sensor Effects

Loglikelihood

LCCD (y | ) (i)i

y(i)ln(i)i

( j) psf(ij

| j)( j)where

L(y | x) LCCD (y | render(x))

• Cascade with

render : x

• Sensor fusion natural; just add loglikelihoods

• CCD loglikelihood of Snyder et. al

Langevin Diffusion Processes

• Fix number of targets and target types• Simulate Langevin diffusion:

)())}(({)( NNXN dWXEdXN

• Distribution of • Computed desired statistics from the samples• Generalizes to non-Euclidean groups like rotations• Gradient computation

– Numeric approximations– Easy and fast on modern 3-D graphics hardware

)()( NNN xX

)}(exp{)( xEx • Write posterior in Gibbs form:

Birth Death Type-change

Jump Processes

• Gibbs style–Sample from a restricted part of the posterior

• Metropolis-Hastings style–Draw a “proposal” from a “proposal density”–Accept (or reject) the proposal with a certain probability

Jump Strategies

Example Jump-Diffusion Process

Average Static State

Average Dynamic State

Thermal Variability

Simulations from PRISM: Discretizes target surface using regions from CAD template and internal heat transfer model

CIS/MIM

Can’t Hide from Thermal VariationsProfile 8 Profile 45 Profile 75 Profile 140

Performance VariationsDue To Thermodynamic Variability

Performance Loss Due ToInaccurate Thermodynamic Information

Cooper, Miller SPIE 97CIS/MIM

Principle Component Representation of Thermal State

• Model radiance as scalar random field on surface • Compute empirical mean & covariance from

database of 2000 radiance profiles• Karhunen-Loeve expansion using eigenfunctions

of covariance on surface - “Eigentanks”• Add expansion coefficients to parameter space

– Fortunately, able to estimate directly given pose

SPIE 97 Cooper, Grenander, Miller, Srivastava

A younger, much thinner AaronLanterman

Matt Cooper(now with Xerox)

CIS/MIM

Meteorological Variation Operational Variation

Composite Mode of VariationSPIE 97 Cooper, Grenander, Miller, Srivastava

The First “Eigentanks”

Remember, we’reshowing 2-D views offull 3-D surfaces

CIS/MIM

Joint MAP Est. of Pose and Thermal SignatureReal

NVESD M60 data (courtesy

James Ratches)

SPIE 98 Cooper and Miller

InitialEstimate

FinalEstimate

CIS/MIM

“Cost” of Estimating Thermal State

MSE Performance LossComanche SNR = 5.08 dB

CIS/MIM

Ladar/IR Sensor FusionMSE Performance Bound Information Bound

LADAR (range)

FLIR(intensity)

Joe KostakisTom Green

Jeff Shapiro

CIS/MIM

LADAR & IR Sensor FusionLADAR & IR Sensor Fusion

10 11 12 13 14 15 16 17 18-28

-26

-24

-22

-20

-18

-16

-14

-12

-10

Ladar CNR (dB)

HSB Performance Curve - 15 deg error

MMSE=0.05

9 10 11 12 13 14 15 16 17 18 19 20-30

-25

-20

-15

-10

-5

Ladar CNR (dB)

HSB Performance Curve - 9 deg error

MMSE=0.05

LADAR/FLIR Hannon Curve 15 degrees error

LADAR/FLIR Hannon Curve 9 degrees error

SPIE 98 Advanced Techniques ATR III Kostakis, Cooper, Green, Miller, OSullivan, Shapiro SnyderCIS/MIM

Target Models

Panzer IILight Tank

Hull Length: 4.81 mWidth: 2.28 mHeight: 2.15 m

Sturmgeschultz IIISelf-Propelled Gun

Hull Length: 6.77 mWidth: 2.95 mHeight: 2.16 m

Semovente M41 Self-Propelled Gun

Hull Length: 5.205 mWidth: 2.2 mHeight: 2.15 m

M48 A3 Main Battle Tank

Hull Length: 6.419 mWidth: 3.63 mHeight: 3.086 m

(Info and Top Row of Images from 3-D Ladar Challenge Problem Slides by Jacobs Sverdrup)

CR-Bound on Orientation

Strum

Semo

Position assumed known

Position unknown, must beco-estimated

Interesting knee at 0.2 meters

We take a performance hit!

M48 vs. Others

M48 and Panzer have dissimilar signatures; most easily distinguished

M48 and Semo have similar signatures; most easily confused

Semovente vs. Others

At higher resolutions,Semo and M48 have most dissimilar signatures; most easily distinguished(perhaps there are nice features which only become apparent at higher resolutions?)

Semo and Sturm have similar signatures; most easily confused

At lower resolutions,Semo and Panzer have most dissimilar signatures; most easily distinguished

JosephO’Sullivan

Synthetic Aperture Radar

MichaelDeVore

•• MSTAR Data Set

• Conditionally Gaussian model for pixel values with variances trained from data

• Likelihood based classification

• Target orientation unknown and uniformly distributed over 360° of azimuth

• Joint orientation estimation and target classification

• Train on 17° depression angle

• Test on 15° depression angleSAR Images Variance Images

T72

BM

P 2

CIS/MIM

• Results using 72 variance images per target of 10° each, and using 80 x 80 pixel sub-images to reduce background clutter

• Probability of correct classification: 98%

• Average orientation error: < 10°

Supported by ARO Center for Imaging Science DAAH 04-95-1-04-94 and ONR MURI N00014-98-1-06-06

2S1 BMP 2 BRDM 2 BTR 60 BTR 70 D7 T62 T 72 ZIL131 ZSU 23 4

2S1 265 0 5 0 0 0 4 0 0 0 BMP 2 0 576 6 4 0 0 0 1 0 0 BRDM 2 2 0 259 0 0 1 1 0 0 0 BTR 60 1 0 1 193 0 0 0 0 0 0 BTR 70 2 2 0 1 191 0 0 0 0 0 D7 2 0 0 0 0 271 1 0 0 0 T 62 2 0 0 0 0 0 265 4 2 0 T 72 0 1 0 0 0 0 4 577 0 0 ZIL131 2 0 0 0 0 0 1 0 271 0 ZSU 23 4 0 0 0 0 0 3 0 1 0 270

2S1 BMP 2 BRDM 2 BTR 60 BTR 70 D7 T62 T 72 ZIL131 ZSU 23 40

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1HS Orientation Error for 72 Windows of 10 Degrees at 80x80

0

4.05

5.73

7.02

8.10

9.06

9.93

10.7

11.4

12.1

12.8

Orientation MSE effects ID!

CIS/MIM

Caveat

Do not confuse the model with reality.

Where Should Clutter Go? (1)

A “forward model,” i.e. a “scene simulator”

)""),(( noiseparamrenderfdata

• A forest might go well in the “noise” part…

non-Gaussian minimax entropy texture models by Song Chun Zhu

Where Should Clutter Go? (2)

)""),(( noiseparamrenderfdata

• …but downtown Baghdad will not “whiten”• Structured clutter is the most vexing• May need to go in here, and directly manipulate the

clutter

…or a bit of each

• Where to draw the line?

Acknowledgments• Much of the work described here was funded by the ARO

Center for Imaging Science

• Also ONR (William Miceli) and AFOSR (Jon Sjogren)

• Slides with CIS/MIM tag were adapted from slides provided by Michael Miller